An anisotropic elastic model for granular materials derived from stress probing tests

This paper develops an anisotropic elastic model for granular materials using the tensor function representative theorem. Based on three-dimensional discrete element simulations, the internal structure is characterized at the particle level, while the elastic stiffness matrix and moduli are determined through stress probing. With all variables in the theorem explicitly derived, the remaining material coefficients, previously determined empirically, can now be quantified. The model’s predictive performance is evaluated using different forms of fabric tensor (normal contact, branch vector, and particle orientation), with comparisons identifying the tensor that best captures elastic anisotropy. To further improve accuracy, the dependence of material coefficients on fabric invariants is incorporated. In addition, within the framework of anisotropic critical state theory, a modified fabric evolution law is proposed to capture the fabric evolution induced by anisotropic stress state, with a specific modification to simulate its rapid evolution observed at the early stages of loading. The integration of anisotropic elasticity with the proposed evolution law enables a comprehensive description of anisotropic stiffness and its progressive variation due to fabric evolution during plastic deformation. Model predictions show good agreement with simulation results, as demonstrated by comparisons of elastic stiffness matrix components, stress response envelopes, anisotropic stiffness ratios, and undrained unloading slopes.